\documentclass[tikz,border=2pt]{standalone}
\begin{document}

\begin{tikzpicture}[scale=2]
\draw[step=1,color=gray!40] (-2,-2) grid (2,2);
\draw[latex-latex, red] (0,-2) -- ++(-1,1) -- ++(-1,-1);
\draw[dashed, blue] (0,1) -- +(-1,1) -- +(-2,0);
\end{tikzpicture}

\end{document}